ISSN:
1432-2234
Keywords:
Helium atom eigenfunctions
;
Fock's expansion
;
Convergence properties
;
Functional analysis
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
Notes:
Abstract It is proved by functional analytic methods that for S-state solutions of Schrödinger's equation for the helium atom, Fock's expansion in powers of R 1/2 and R ln R, where R is the hyperspherical radius r 1 2 +r 2 2 , converges pointwise for all R, thereby generalising a result of Macek that the expansion converges in the mean for all R〈1/2. It is shown that for any value (even complex) of the energy E, Schrödinger's equation, considered as a partial differential equation with no boundary condition at R=∞, has infinitely many solutions representable by an expansion of the type proposed by Fock. Some of the open problems are discussed in determining whether for E in the point spectrum of the atomic Hamiltonian the physical eigenfunction ΨE, which has exponential decay as R →∞, is representable by Fock's expansion.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00526420
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